3) Resolva as seguintes inequações em R:
a) 2(x + 3) > 3 (1 - x)
b) 3(1 - 2x) < 2(x + 1) + x - 7
c) x/3 - (x+1)/2 < (1 - x) / 4
d) (x + 3) > (-x-1)
e) [1 - 2*(x-1)] < 2
f) 6x + 3 < 3x + 18
g) 8(x + 3) > 12 (1 - x)
h) (x + 10) > ( -x +6)
Soluções para a tarefa
2x - 2x + 6 > 3 - 3x - 2x
6 - 3 > -5x
3 > - 5x
-x < 3/5
x > -3/5
b)3 - 6x < 2x + 2 + x - 7
-6x - 3x < -8
-9x < -8
9x > 8
x > 8/9
c) 4x/12 __ 6* (x + 1)/12 < 3*(1 - x)/12
4x - 6r - 6/12 < 3 - 3x/12
-2x - 6 < 3 - 3x
x < 9
d) x + 3 > -x - 1
2x > -4
x > -4/2
x > -2
e)1 - 2x + 2 < 2
- 2x < 2 - 1 - 2
- 2x < -1
2x > 1
x > 1/2
f) 6x - 3x < 18 - 3
3x < 15
x < 15/3
x < 5
g) 8x + 24 > 12 - 12x
20x > 12 - 24
20x > -12
x > -12/20
x > -3/5
h) x + x > 6 - 10
2x > -4
x > -4/2
x > -2
vamos aos cálculos:
a) 2(x + 3) > 3 (1 - x)
2x + 6 > 3 - 3x
5x > -3
x > -3/5
b) 3(1 - 2x) < 2(x + 1) + x - 7
3 - 6x < 2x + 2 + x - 7
-9x < -8
9x > 8
x > 8/9
c) x/3 - (x+1)/2 < (1 - x) / 4
4x/12 - 6* (x + 1)/12 < 3*(1 - x)/12
4x - 6x -6 < 3 - 3x
x < 9
d) (x + 3) > (-x-1)
2x > -4
x > -4/2
x > -2
e) [1 - 2*(x-1)] < 2
1 - 2x + 2 < 2
- 2x < -1
2x > 1
x > 1/2
f) 6x + 3 < 3x + 18
3x < 15
x < 15/3
x < 5
g) 8(x + 3) > 12 (1 - x)
8x + 24 > 12 - 12x
20x > -12
x > -12/20
x > -3/5
h) (x + 10) > ( -x +6)
2x > -4
x > -4/2
x > -2